No, the Citrix ICA client (nowadays called Receiver / Online plug-in) works like Microsoft's RDP: it sends mouse/keyboard commands from your PC to the XenApp server, but only those regarding the published application or the published desktop you are working with. There is no logging facility built into XenApp of data outside the actual session on the remote server.
There are ways, however, of viewing and recording the screen of the XenApp server session without you knowing. But if I understood your question correctly that was not what you wanted to know.
Let me know if you need more information.